1. adjective. Crazy. But not violently dangerous or otherwise scarry crazy. Often means only that a person is a little odd. Amusingly eccentric. Barmy, bats, batty, bonkers, buggy, cracked, crackers, daft, fruity, kooky, loco, loony, loopy, nuts, nutty, round the bend, or wacky. (We've got a lot of words for the half-way crazies). She's dotty!

2. adjective. Having a feeble or unsteady walk (especially animals); shaky, gimpy. My horse is a bit dotty.

3. adjective. Obsessively infatuated. He's dotty over her.

Etymology: Probably from the Scottish dottle, meaning silly, which in turn comes from the Middle English doten, meaning to dote.

Thanks to Dictionary.com for the synonyms and etymology.

Dot"ty (?), a. [From 2d Dot.]

1.

Composed of, or characterized by, dots.

2. [Perh. a different word; cf. Totty.]

Unsteady in gait; hence, feeble; half-witted. [Eng.]

 

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